Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void data() {}
const int N = 1e6 + 100;
const long long mod = 998244353;
const long long mod2 = 1e9 + 7;
int main() {
  data();
  long long n;
  cin >> n;
  map<long long, long long> was;
  for (long long i = 1; i <= 1e5; i++) {
    was[i * i + i] = 1;
  }
  n *= 2;
  for (long long i = 1; i <= 1e5; i++) {
    long long kek = n - (i * i);
    kek -= i;
    if (was[kek] && kek > 0) {
      cout << "YES";
      return 0;
    }
  }
  cout << "NO\n";
}